Definition 2.4 ([1]}) 
Let \(\eta ,\,m \in \mbox{R}\)  and \(l\in  such that \) >0, m>0\( and \) (jm+l)+1-1,-2,-3,(j=0,1,2,) \(. Then generalized (Kilbas--Saigo) Mittag--Leffler type function of three parameters is defined by\)\( \mathcal {E}_{\eta ,\,m,\,l}\,(z)= \sum _{k=0}^{\infty } c_k\, z^k \)\(where \)\( c_{0} =1, ~c_{k}=\prod _{j=0}^{k-1}\frac{\Gamma (\eta [jm+l]+1)}{\Gamma (\eta [jm+l+1]+1)}\,\,(k=1,2,\cdots )\)\(and an empty product is assumed to be equal to one.\)
